If you have an aftermarket muffler you might get some change in sound. I had a Flowmaster super 40 on stock pipes and had a wicked drone at 1500 RPM. After I dumped it over the axle I lost the drone and the exhaust note was actually a little quieter. And yes if you leave your truck running while stopped you will get some build up of exhaust gas under the bed.

In some cases, depending on where you cut, it can also heat up the axel housing, and cause premature wear/failure of parts in the axel.

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X2 gazillion billion....!!!!!!!!!!!

I had to cut my exhuast right behind the muffler due to trail damage....as a result the hot gasses dumped right onto the housing....the housing got so that my ABS sensor wires actualy melted. I also now thinking that as Chris4x4 mentioned, all that excessive heat in ghe heat as a result may have contributed to my rear ring and pinion failures. I have recently added a small turndown pipe that I purchased from pep boys to help direct the exhaust gasses away from the axle housing